Question

9 ^-4*4 ^-4/2 ^-9*3 ^-9=

Answer 1

Ответ:

Ответ и решение в закрепе

Answer 2

To simplify the expression 9^(-4) * 4^(-4) / 2^(-9) * 3^(-9), we can use the properties of exponents.

Recall that a negative exponent indicates the reciprocal of the base raised to the positive exponent. So, we can rewrite the expression as follows:

(1/9^4) * (1/4^4) / (1/2^9) * (1/3^9)

To simplify further, we can combine the fractions by multiplying the numerators and denominators:

[(1 * 1 * 1 * 1) / (9 * 9 * 9 * 9)] * [(1 * 1 * 1 * 1) / (4 * 4 * 4 * 4)] / [(1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1) / (2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2)] * [(1 * 1 * 1 * 1 * 1 * 1 * 1 * 1 * 1) / (3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3)]

Simplifying further, we get:

(1 / 6561) * (1 / 256) / (1 / 512) * (1 / 19683)

To divide fractions, we multiply by the reciprocal of the second fraction:

(1 / 6561) * (1 / 256) * (512 / 1) * (1 / 19683)

Simplifying the numerators and denominators:

(512 / 6561) * (1 / 256) * (1 / 19683)

Multiplying the fractions:

(512 * 1 * 1) / (6561 * 256 * 19683)

Simplifying the numerator and denominator:

512 / (3361997594624 * 256)

Finally, evaluating the division:

512 / 861989870786304

The simplified value of the expression is approximately 5.941762389642e-16.